ebook img

Analytical reasoning with multiple external representations PDF

268 Pages·2002·1.57 MB·English
by  
Save to my drive
Quick download
Download
Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.

Preview Analytical reasoning with multiple external representations

Analytical reasoning with multiple external representations Richard Cox U N I VER E S I H T T Y O H G F R E U DI N B Ph.D. University of Edinburgh 1996 Abstract This thesis presents work on analytical reasoning with external representations (ERs) using problems similar to those used in the US GRE college-entrance examination. The work investigates the factors associated with e(cid:11)ective ER use in situations where subjectsselect, constructand reasonwiththeir ownERs. Practically all previous work has tended to focus solely upon performance rather than process. In this thesis the emphasis is upon cognitive processes during the entire time-course of reasoning with ERs, from problem comprehension through to answer selection. A background to the work is provided by 2 comprehensive reviews of: 1.) previous research on ERs and reasoning and 2.) the cognitive and semantic properties of ERs. Results from three empirical studies are reported. The (cid:12)rst study examined a large corpusof‘workscratchings’produced bysubjectsastheysolvedpaperandpencil-based analytical reasoning problems under test conditions. The workscratching ERs showed great diversity between and within subjects and across a range of problems. They included lists, various kinds of table, set diagrams, node and arc diagrams, (cid:12)rst-order and propositional logic, plans and natural language. It is shown that problem-solving performance is related to the type of ER used in the solution. The second study utilised a computer-based system (switchERI). The system admin- istered analytical reasoning problems and provided a range of ER construction envi- ronments for the subject to choose and switch between. User-system interactions were recorded dynamically during problem solving. This methodology permitted micro- analyses of the cognitive events at each stage during the time-course of problem solv- ing. A process account of analytical reasoning with ERs is developed in which (cid:12)ve major stages are identi(cid:12)ed - problem comprehension, ER selection, ER construction, read-o(cid:11) from the ER and answer selection/responding. A range of common slips and misconceptions are identi(cid:12)ed at each stage. The results show, inter alia, that subjects whose responses are consistent with their ERs perform better than subjects whose responses are inconsistent with their ERs even if the ER is partially incorrect. The data from the workscratching analysis and switchERI study informed the design of switchERII, a second system. SwitchERII incorporates a representation of the semantics of Euler’s Circles, dynamically parses the user’s representation and provides feedback and advice. A third study was conducted with the switchERII system. Few, if any, studies to date have attempted to relate subjects’ prior knowledge of ER formalismstotheirreasoningperformance. Subjects’priorknowledgeofERformalisms was assessed in both switchER studies. It was observed that subjects’ performance on representation interpretation tasks does not necessarily predict their performance in conditions where they select and construct their own representations. The reasons for the decoupling are discussed. Data from all three studies show that subjects often utilise multiple representations in their solutions, either concurrently or serially via ER switching. Two distinctly di(cid:11)erent types of switching were observed. One kind (‘thrashing’) is associated with poorer performance and re(cid:13)ects less comprehensive prior knowledge, inability to select anappropriateERandhazyproblemcomprehension. Judicious switching,ontheother hand, is associated with high levels of problem comprehension and skilled matching of ii the ERs’ properties to changing task demands. It is claimed that e(cid:11)ective reasoning with ERs involves complex interactions between at least three factors: (a.) within-subject variables such as the subject’s representa- tionalrepertoire(priorknowledge)andrepresentationalmodalitypreferences(cognitive style); (b.) skill at overcoming a variety of barriers to comprehension and an ability to discern the salient attributes and characteristics of di(cid:11)erent problem types and (c.) an understanding of the semantic and cognitive properties of graphical and non-graphical ERs coupled with an ability to match those properties to the problem’s task demands. It is suggested that the role of externalisation in reasoning with ERs may be to fa- cilitate the swapping of information between cognitive subsystems. A mechanism by which the use of diagrammatic ERs may facilitate self-explanation is also proposed. Thethesis concludes with anargumentin favourofadomain-independent ‘ERcurricu- lum’ . It is suggested that direct instruction in the use of a range of ERs might equip students with wider representational repertoires and hence allow them more scope to indulge their representational preferences. Finally, several directions for future work are proposed. These include extending the representational semantics of switchERII, evaluating various types of system feedback and implementing a mechanism for check- ing for slips during read-o(cid:11) from ERs. iii Acknowledgements This thesis is dedicated to my family. Many individuals are owed my thanks and gratitude for helping bring this thesis to its conclusion. First, profound and special thanks are due to my primary supervisor, Dr. Paul Brna, for many hours of patient help and supervision and for being a constant source of advice and encouragement. Secondly, IwouldliketothankmyworkcolleaguesintheGraphicsandLanguageWork- ing Group of the Human Communication Research Centre - Professor Keith Stenning (my second supervisor), Drs. Corin Gurr, Robert Inder, John Lee, Jon Oberlander, andRichardTobinforinnumerable stimulatingdiscussions, somein formalsettingsbut mostly in our o(cid:14)ces and in the tea room! I also acknowledge the invaluable assistance A that Robert and Richard gave me with Prolog and LTEX. Thanks, for many stimulating discussions in Cellar One (and more formal settings), to my friends and colleagues in the A.I. and Education and COED groups, especially Maziah Aziz, Diana Bental, Susan Bull, David Duncan and Judith Good. I also wish to thank everyone who participated in my experiments. I must also express gratitude to Dr. Helen Pain and Professor Rosamund Sutherland for agreeing to formally examine the thesis. I would also like to acknowledge the continuing in(cid:13)uence of my Masters degree super- visor, Dr. Tom Matyas (School of Behavioural Health Sciences, La Trobe University, Australia). I remain indebted to him for any skills in research methods and statistics that I may possess. Thanks too to Dr. Geo(cid:11) Cumming of the Psychology Department for many useful and thought-provoking discussions. Finally, I am indebted to Dr. Carmel Lum, my dear friend and partner of 19 years, whose love and constant encouragement enabled me to realise my aspirations. iv Declaration I hereby declare that I composed this thesis entirely myself and that it describes my own research. Richard Cox Edinburgh December 4, 1996 Some of the work in this thesis was published prior to thesis submission. Some of the analyses of ‘workscratchings’ presented in Chapter 5 and the switchERI study described in Chapter 6 appeared as: Cox, R. & Brna, P. [1995] Supporting the use of external representations in prob- lem solving: The need for (cid:13)exible learning environments. Journal of Arti(cid:12)cial Intelligence in Education, 6(2), 239{302. Some of the workscratching analyses reported in Chapter 5 were also reported in: Cox, R., Stenning, K. & Oberlander, J. [1995] The e(cid:11)ect of graphical and sen- tential logic teaching on spontaneous external representation. Cognitive Studies: Bulletin of the Japanese Cognitive Science Society, 2(4), 56{75. Several conference papers were also based on the work: Cox, R.J. & Brna, P. [1993] Reasoning with external representations: Supporting the stages of selection, construction and use. Proceedings of the World Con- ference on Arti(cid:12)cial Intelligence in Education (AI-ED93), Charlottesville, VA: Association for the Advancement of Computing in Education, 185-192. Cox, R.J. & Brna, P. [1993] Analytical reasoning with external representations: The relationship between prior knowledge and performance. In R.Cox, Petre, M., Brna, P. and Lee, J. Proceedings of the workshop on Graphical represen- tations, reasoning and communication held at World Conference on Arti(cid:12)cial Intelligence and Education (AI-ED93), August, Edinburgh, 33-36. Cox, R. & Draper, S. [1995] External representations, choice and task e(cid:11)ective- ness. 4th ESRC Seminar on internal and external representations (Representa- tions and Constructivism), Institute of Education, London, 21-22 April, 1995. v Cox, R. [1996] The role of externalisation in reasoning with self-constructed repre- sentations. Presented at the IEE Colloquium on Thinking with Diagrams,Savoy Place, London, January 18. IEE Digest No. 96/010, London: Institute of Elec- trical Engineers, 1{7. The following Departmental papers were also based on the work: Cox, R.J. & Brna, P. [1993] The relationship between prior knowledge of external representationsandanalyticalreasoningperformance: Implications forthedesign of a learning environment. Research Paper RP-646, Department of Arti(cid:12)cial Intelligence, University of Edinburgh. Cox, R. & Brna, P. [1994] Analyticalreasoningwithexternalrepresentations: Sup- porting the stages of selection, construction and use. Research Paper RP-686, Department of Arti(cid:12)cial Intelligence, University of Edinburgh. vi Contents Abstract iii Acknowledgements iv Declaration vi List of Figures viii 1 Introduction 1 What this thesis is about . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 What this thesis is not about . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 De(cid:12)ning the term ‘external representation’ . . . . . . . . . . . . . . . . . . . 5 ER taxonomies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Conceptualisations of representations in related (cid:12)elds . . . . . . . . . . . . . . 11 Representations in mathematics and arti(cid:12)cial intelligence . . . . . . . . 11 Representations and psychology, cognitive science . . . . . . . . . . . . . 15 Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2 The domain: Analytical reasoning problems 25 The characteristics of analytical reasoning problems . . . . . . . . . . . . . . 25 Attractiveness of the domain . . . . . . . . . . . . . . . . . . . . . . . . 28 The linguistic and structural properties of analytical reasoning problems. 29 3 Stages in analytical reasoning with ERs 32 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Interpretation and comprehension . . . . . . . . . . . . . . . . . . . . . . 33 vii ER selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 ER construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Read-o(cid:11) from ER and responding . . . . . . . . . . . . . . . . . . . . . . 58 Summary and conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4 Related work 66 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 ER construction by the subject: studies utilising domain-speci(cid:12)c ER forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 ER construction by the subject: studies utilising non domain-speci(cid:12)c ER forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Studies in which subjects used prefabricated ERs . . . . . . . . . . . . . 79 Review conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 ERs and ILEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Thesis arguments expounded in detail . . . . . . . . . . . . . . . . . . . . . . 88 ER selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Constructivism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Switching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Summary of aims of (cid:12)rst study . . . . . . . . . . . . . . . . . . . . . . . 93 5 An investigation of ER use in reasoning. 95 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Issues of validity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Problem selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Results and Discussion | Workscratching Corpus . . . . . . . . . . . . 99 Multiple representations . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Summary and Conclusions | Workscratching Data. . . . . . . . . . . . 109 6 SwitchERI - an ILE for analytical reasoning. 112 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 viii Prior knowledge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Method and Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 Task Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Summary and Conclusions | switchERI study . . . . . . . . . . . . . . . . . 134 Implications for the Design of an Interactive Learning Environment (ILE)135 Support at the Problem Comprehension Stage. . . . . . . . . . . . . . . 136 Support at the Representation Selection Stage. . . . . . . . . . . . . . . 136 Supporting ER Construction . . . . . . . . . . . . . . . . . . . . . . . . 139 Supporting the Use of the ER in Question Answering . . . . . . . . . . . 142 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 7 SwitchERII { an intelligent ILE. 145 switchERII development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Pilot study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 184 8 General thesis discussion 187 Summary of what has been achieved . . . . . . . . . . . . . . . . . . . . . . . 187 Problem comprehension . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 ER selection & construction . . . . . . . . . . . . . . . . . . . . . . . . . 190 Constructivism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 Individual di(cid:11)erences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 The way forward - future work . . . . . . . . . . . . . . . . . . . . . . . . . . 198 Graphics curriculum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 9 Conclusion 204 Thesis contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 ix Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 10 References 209 A 227 Three examples of analytical reasoning problems . . . . . . . . . . . . . . . . 227 Example ERs - workscratching (cid:12)gures . . . . . . . . . . . . . . . . . . . . . . 230 Single Models | Ignoring Alternatives . . . . . . . . . . . . . . . . . . . . . . 246 ‘Invented’ Annotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 The Use of Multiple Representations . . . . . . . . . . . . . . . . . . . . . . . 248 Representation recommended by Brownstein et al. for Problem 2 . . . . . . . 250 Eighty-seven stimulus items used in the switchERI study taxonomy pre-task 251 Euler’s circle interpretation task data from switchERII study. . . . . . . . . . 254 B 255 Publications bound into thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 255 x

Description:
ERs, from problem comprehension through to answer selection. A background A process account of analytical reasoning with ERs is developed in which ve major stages .. Supporting the Use of the ER in Question Answering .
See more

The list of books you might like

Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.